Institute for Pure & Applied Mathematics (IPAM) Courses

Deep Operator Learning Approximation and Distributed Applications

Explore neural operators for solving PDEs, error convergence analysis, and distributed learning algorithms for heterogeneous multiscale functions and multi-operator settings.

• YouTube
• 38 minutes
• Self-Paced
• Free Video

Sampling, Inference, and Data-Driven Physical Modeling in Scientific Machine Learning

Discover advanced sampling and inference techniques for data-driven physical modeling in scientific machine learning applications.

• YouTube
• 37 minutes
• Self-Paced
• Free Video

Learning-Enhanced Structure Preserving Particle Methods for Landau Equation

Explore deep learning-enhanced particle methods for solving the complex Landau equation in plasma physics, combining traditional structure-preserving techniques with neural networks.

• YouTube
• 32 minutes
• Self-Paced
• Free Video

Score-Based Generative Models through the Lens of Wasserstein Proximal Operators

Explore score-based generative models as Wasserstein proximal operators through mean-field games, featuring kernel-based approaches for enhanced training efficiency and manifold learning.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Probabilistic Operator Learning - Generative Modeling and Uncertainty Quantification

Discover probabilistic operator learning through ICON networks for Bayesian inference in differential equations, enabling uncertainty quantification and generative modeling.

• YouTube
• 40 minutes
• Self-Paced
• Free Video

Unsupervised In-Context Operator Learning for Mean Field Games

Discover unsupervised in-context operator learning for solving high-dimensional mean field games efficiently without discretization or supervised labels in a single forward pass.

• YouTube
• 39 minutes
• Self-Paced
• Free Video

A Supervised Learning Scheme for Hamilton-Jacobi Equation via Density Coupling

Discover a supervised learning approach for solving high-dimensional Hamilton-Jacobi PDEs using Wasserstein Hamiltonian flows and density coupling strategies.

• YouTube
• 40 minutes
• Self-Paced
• Free Video

Mixed-Precision Algorithms for Training Neural ODEs

Discover mixed-precision algorithms for training Neural ODEs, reducing computational costs while maintaining stability and accuracy in scientific machine learning applications.

• YouTube
• 37 minutes
• Self-Paced
• Free Video

Tracking Bacterial Growth Using a Nonlocal Interfacial Model

Explore nonlocal interfacial modeling techniques for tracking bacterial colony formation and arrested fronts in biological pattern formation systems.

• YouTube
• 36 minutes
• Self-Paced
• Free Video

Exploiting Low-Dimensional Data Structures and Understanding Neural Scaling Laws of Transformers

Explore how low-dimensional data structures explain transformer scaling laws through statistical estimation theory and empirical validation with large language models.

• YouTube
• 41 minutes
• Self-Paced
• Free Video

Characteristic-Based Deep Learning Framework for Hamilton-Jacobi Equations and Optimal Transport

Discover a novel deep learning framework for solving Hamilton-Jacobi PDEs using characteristic methods, with applications to optimal transport problems and high-dimensional solutions.

• YouTube
• 36 minutes
• Self-Paced
• Free Video

Fast, Accurate and Large-Scale Ab-Initio Calculations for Materials Modeling

Explore advanced computational methods for large-scale density functional theory calculations, their applications in materials modeling, and the performance of the DFT-FE open-source code.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

The Pitfalls of Using ML-Based Optimization - IPAM at UCLA

Explore pitfalls of ML-based optimization in graph problems, comparing traditional approaches for Force Path Cut and Hypergraph Discovery. Gain insights on limitations and potential improvements in AI applications.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

Discrete Optimization-Aided Structured Learning at Scale - IPAM at UCLA

Explore discrete optimization techniques for structured learning, featuring algorithmic aspects, statistical setups, and approaches to feature selection and learning trees.

• YouTube
• 56 minutes
• Self-Paced
• Free Video

Optimization-in-the-Loop AI for Energy and Climate - IPAM at UCLA

Optimization-in-loop AI framework for climate action: enhancing ML models with physics, constraints, and decision-making processes for energy grids, building efficiency, and more.

• YouTube
• 1 hour
• Self-Paced
• Free Video